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A STORAGE SYSTEM WITH SPORADIC AND CONTINUOUS CLEARINGS

Published online by Cambridge University Press:  22 October 2007

Wolfgang Stadje
Wolfgang Stadje
Affiliation:
Universität OsnabrückFachbereich Mathematik/Informatik 49069 Osnabrück, Germany E-mail: wolfgang@mathematik.uos.de
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Abstract

We study a cumulative storage system that is totally cleared sporadically at stationary renewal times and whenever a finite-capacity threshold is exceeded. The independent and identically distributed inputs occur at time epochs that also form a stationary renewal process. We determine the distribution of the interoverflow times. Although this distribution is quite intricate when both underlying renewal processes are general, in the special case of Poisson sporadic clearings we obtain a neat formula for its Laplace transform.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 21 , Issue 4 , October 2007 , pp. 539 - 549
Copyright
Copyright © Cambridge University Press 2007

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References

1.Artalejo, J.R. & Gomez-Corral, A. (1998). Analysis of a stochastic clearing system with repeated attempts. Stochastic Models 14: 623–645.CrossRefGoogle Scholar
2.Berman, O., Parlar, M., Perry, D., & Posner, M.J.M. (2005). Production/clearing models under continuous and sporadic reviews. Methodology and Computing in Applied Probability 7: 203–225.CrossRefGoogle Scholar
3Boxma, O.J., Perry, D., & Stadje, W. (2001). Clearing models for M/G/1 queues. Queueing Systems 38: 287–306.Google Scholar
4.El-Taha, M. (2002). A sample-path condition for the asymptotic uniform distribution of clearing processes. Optimization 51: 965–975.Google Scholar
5.Kim, K., & Seila, A.F. (1993). A generalized cost model for stochastic clearing systems. Computers and Operations Research 20: 67–82.Google Scholar
6.Liu, B. & Cao, J. (1999). Analysis of a production-inventory system with machine breakdowns and shutdowns. Computers and Operations Research 26: 73–91.CrossRefGoogle Scholar
7.Moinzadeh, K. & Aggarwal, P. (1997). Analysis of a production/inventory system subject to random disruptions. Management Science 43: 1577–1588.CrossRefGoogle Scholar
8.Perry, D. & Posner, M.J.M. (2002). Production-inventory models with an unreliable facility operating in a two-state random environment. Probability in the Engineering and Informational Sciences 16: 325–338.Google Scholar
9.Perry, D., Stadje, W., & Zacks, S. (2005). Sporadic and continuous clearing policies for a production/inventory system under an M/G demand process. Mathematics of Operations Research, 30: 354–368.Google Scholar
10.Serfozo, R. & Stidham, S. (1978). Semi-stationary clearing processes. Stochastic Processes and Their Applications 6: 165–178.Google Scholar
11.Stidham, S. (1974). Stochastic clearing systems. Stochastic Processes and Their Applications 2: 85–113.CrossRefGoogle Scholar
12.Stidham, S. (1977). Cost models for stochastic clearing systems. Operations Research 25: 100–127.CrossRefGoogle Scholar
13.Stidham, S. (1986). Clearing systems and (s, S) inventory systems with nonlinear costs and positive lead times. Operations Research 34: 276–280.CrossRefGoogle Scholar
14.Wang, J., Cao, J., & Liu, B. (2002). Unreliable production-inventory model with a two-phase Erlang demand arrival process. Computers and Operations Research 43: 1–13.Google Scholar
15.Whitt, W. (1981). The stationary distribution of a stochastic clearing process. Operations Research 29: 294–308.Google Scholar
16.Yang, W.S., Kim, J.D., & Chae, K.C. (2002). Analysis of M/G/1 stochastic clearing systems. Stochastic Analysis and Applications 20: 1083–1100.CrossRefGoogle Scholar